How to solve for an unknown sine wave

On 4/29/2010 10:23:36 AM, dmradcliff wrote:
>I have data collected from an
>oscilloscope and I am trying
>to create an ideal sine wave
>to match the collected data.
>I need to solve for amplitude,
>frequency, phase, and DC
>offset. (n = amplitude * sine
>(frequency * x + phase) +
>offset)
>
...
>Thanks,
>Dale
_______________________________

Alternately and in conjonction to "ideal sine", it's probably possible to run a spline smoothlet. Comparing both will result in an analytical "deviation function" which is in fact of more indicative value than a simple residual bar plot. All discrete filtering/smoothing do distort. Your project as a typical demo might takes only few minutes.

jmG

Sounds like a job for an FFT (CFFT?)
Fred Kohlhepp
fkohlhepp@sikorsky.com

See the worksheet here:

http://collab.mathsoft.com/read?124003,63

Richard

You can set up a solve block equating a vector evaluation of your function (with parameters) to the measurements, or use minerr. Check out the help and the Quicksheet examples.

You need to give initial estimates of all the paramters. You can estimate amplitude from the max-min of measurements, take the mean as an offset estimate. Use one of the DFT functions to estimate freq (compute from the index at max magntude). I think you can start with any phase (e.g. zero) and get convergence if the other parameters are reasonably estimated.

For any automated process, I recommend that you compute the actual error/goodness-of-fit given by the purported solution (with actions as appropriate) just to make sure the solving algorithm hasn't put you off in deep space.

If you still have trouble, post an example worksheet with whatever you have done.

Lou